The response of a Duffing-van der Pol oscillator under delayed feedback control

Li, X; Ji, JC; Hansen, CH; Tan, C

The response of a Duffing-van der Pol oscillator under delayed feedback control

Li, X Ji, JC

Hansen, CH Tan, C

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Publication Type:: Journal Article
Citation:: Journal of Sound and Vibration, 2006, 291 (3-5), pp. 644 - 655
Issue Date:: 2006-04-04

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Field	Value	Language
dc.contributor.author	Li, X	en_US
dc.contributor.author	Ji, JC https://orcid.org/0000-0003-3280-5463	en_US
dc.contributor.author	Hansen, CH	en_US
dc.contributor.author	Tan, C	en_US
dc.date.issued	2006-04-04	en_US
dc.identifier.citation	Journal of Sound and Vibration, 2006, 291 (3-5), pp. 644 - 655	en_US
dc.identifier.issn	0022-460X	en_US
dc.identifier.uri	http://hdl.handle.net/10453/15275
dc.description.abstract	The nonlinear dynamics of a Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay are investigated. By means of the averaging method and Taylor expansion, two slow-flow equations for the amplitude and phase of the primary resonance response are derived, from which the relations between the amplitude and phase of the primary resonance response and all other parameters are obtained, respectively. The singularity analysis of the equation governing the amplitude of the primary resonance response shows that the bifurcation modes are perturbations of the pitchfork bifurcation. Conditions preventing multiple solutions, corresponding to two different kinds of bifurcation modes, are given, since cases for which multiple solutions are available should be avoided. The stable condition for steady-state response is also given by the Routh-Hurwitz criterion. It is also shown that coupled nonlinear state feedback control can be replaced by uncoupled nonlinear state feedback control. © 2005 Elsevier Ltd. All rights reserved.	en_US
dc.relation.ispartof	Journal of Sound and Vibration	en_US
dc.relation.isbasedon	10.1016/j.jsv.2005.06.033	en_US
dc.subject.classification	Acoustics	en_US
dc.title	The response of a Duffing-van der Pol oscillator under delayed feedback control	en_US
dc.type	Journal Article
utslib.citation.volume	3-5	en_US
utslib.citation.volume	291	en_US
utslib.for	091304 Dynamics, Vibration and Vibration Control	en_US
utslib.for	02 Physical Sciences	en_US
utslib.for	09 Engineering	en_US
dc.location.activity	New Zealand
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Mechanical and Mechatronic Engineering
utslib.copyright.status	closed_access
pubs.issue	3-5	en_US
pubs.publication-status	Published	en_US
pubs.volume	291	en_US

Abstract:

The nonlinear dynamics of a Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay are investigated. By means of the averaging method and Taylor expansion, two slow-flow equations for the amplitude and phase of the primary resonance response are derived, from which the relations between the amplitude and phase of the primary resonance response and all other parameters are obtained, respectively. The singularity analysis of the equation governing the amplitude of the primary resonance response shows that the bifurcation modes are perturbations of the pitchfork bifurcation. Conditions preventing multiple solutions, corresponding to two different kinds of bifurcation modes, are given, since cases for which multiple solutions are available should be avoided. The stable condition for steady-state response is also given by the Routh-Hurwitz criterion. It is also shown that coupled nonlinear state feedback control can be replaced by uncoupled nonlinear state feedback control. © 2005 Elsevier Ltd. All rights reserved.

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http://hdl.handle.net/10453/15275